if the perimeter of a circular sector is fixed at 100 ft, what values of r and s give the sector the greatest area?

Question

anonymous · Answer

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anonymous · Answer

PLEASE HELP! WE HAVE A QUIZ TMMR AND THIS WILL DECIDE OUR GRADE

anonymous · Answer

write an equation for the area of the sector in terms of r and S, then maximise. bewm.

anonymous · Answer

how do you write the area of a sector?

paxpolaris · Answer

$$S= {\theta \over360°}\cdot2\pi r$$
area of sector:$$A={\theta \over 360°} \pi r^2$$

anonymous · Answer

how do we find theta?

paxpolaris · Answer

$$A={S \cdot r \over2}$$

paxpolaris · Answer

S+r+r=100

paxpolaris · Answer

so S= 100-2r
so, $$A= {(100-2r)r \over 2}=50r-r^2$$

paxpolaris · Answer

find the maximum of that.

anonymous · Answer

dude you are a pro! thanks so much!!

paxpolaris · Answer

you didn't have to find theta,  as you can combine the original formulae of arc-S and area-A

You should get r = 25, S=50

anonymous · Answer

yeah thanks! we figured it out :)